Finance 410, Homework 3

Rank the following from highest average historical standard deviation to lowest average historical standard deviation from 1926 to 2010. I. Small stocks II. Long-term bonds III. Large stocks IV. T-bills

I, III, II, IV

You have $500,000 available to invest. The risk-free rate, as well as your borrowing rate, is 8%. The return on the risky portfolio is 16%. If you wish to earn a 22% return, you should _________.

y × .16 + (1 - y) × .08 = .22 .16 y - .08 y + .08 = .22 .08 y = .14 y = 1.75 Put 1.75 × $500,000 = $875,000 in the risky asset by borrowing $375,000.

You have the following rates of return for a risky portfolio for several recent years. Assume that the stock pays no dividends # Bought YR Beg Yr Price or sold 2008, 50.00 100B 2009 55.00 50B 2010 51.00 75S 2011 54.00 75S What is the Geometric Average return for the period?

yr 1 (55-50)/50 = 10% yr 2 (51-55)/55 = -7.27% yr 3 (54-51)/51= 5.88% [(1.10)(1 + -.0727)(1.0588)]⅓ - 1 = 2.60%

Your investment has a 20% chance of earning a 30% rate of return, a 50% chance of earning a 10% rate of return, and a 30% chance of losing 6%. What is your expected return on this investment?

(.2)(30%) + (.5)(10%) + (.3)(-6%) = 9.2%

A portfolio with a 25% standard deviation generated a return of 15% last year when T-bills were paying 4.5%. This portfolio had a Sharpe ratio of ____.

(15-4.5)/25 = .42

You purchased a share of stock for $29. One year later you received $2.25 as dividend and sold the share for $28. Your holding-period return was _________.

(28+2.25-29)/29= 4.31%

You have the following rates of return for a risky portfolio for several recent years. Assume that the stock pays no dividends # Bought YR Beg Yr Price or sold 2008, 50.00 100B 2009 55.00 50B 2010 51.00 75S 2011 54.00 75S What is the dollar weighted return for the period?

-50(100)/(1+IRR)^0 + -55(50)/(1+IRR)^1 + 75(51)/(1+IRR)^2 + 54(75)/(1+IRR)^3 + Irr= .744%

You invest $10,000 in a complete portfolio. The complete portfolio is composed of a risky asset with an expected rate of return of 15% and a standard deviation of 21% and a Treasury bill with a rate of return of 5%. How much money should be invested in the risky asset to form a portfolio with an expected return of 11%?

15y + 5(1 - y) = 11; y = 60%; .60(10,000) = $6,000

Consider a Treasury bill with a rate of return of 5% and the following risky securities: Security A: E(r) = .15; variance = .0400 Security B: E(r) = .10; variance = .0225 Security C: E(r) = .12; variance = .1000 Security D: E(r) = .13; variance = .0625

A has the steepest slope, found as: Slope = (.15 − .05)/(.04).5 = .5000

Rank the following from highest average historical return to lowest average historical return from 1926 to 2010. I. Small stocks II. Long-term bonds III. Large stocks IV. T-bills

I, III, II, IV

You are considering investing $1,000 in a complete portfolio. The complete portfolio is composed of Treasury bills that pay 5% and a risky portfolio, P, constructed with two risky securities, X and Y. The optimal weights of X and Y in P are 60% and 40% respectively. X has an expected rate of return of 14%, and Y has an expected rate of return of 10%. To form a complete portfolio with an expected rate of return of 8%, you should invest approximately __________ in the risky portfolio. This will mean you will also invest approximately __________ and __________ of your complete portfolio in security X and Y,

E(rp) = .6(14) + .4(10) = 12.4% .08 = wrp(.124) + (1 - wrp)(.05) wrp ≈ 40% wx in complete portfolio = .40(.60) = 24% wy in complete portfolio = .40(.40) = 16%

You have an EAR of 9%. The equivalent APR with continuous compounding is _____.

LN[1 + .09] = 8.62%

The price of a stock is $55 at the beginning of the year and $50 at the end of the year. If the stock paid a $3 dividend and inflation was 3%, what is the real holding-period return for the year?

Nominal return on stock: (50 + 3)/55 - 1 = −3.64% Real return: (1 + R) = (1 + r)(1 + i) 1 + r = (1 - .0364)/(1.03) = .935 R = .935 - 1 = -.0644

A security with normally distributed returns has an annual expected return of 18% and standard deviation of 23%. The probability of getting a return between -28% and 64% in any one year is _____.

Note that the expected return minus 2 standard deviations is 18% - (2 × 23%) = -28% and the expected return plus 2 standard deviations is 18% + (2 × 23%) = 64%. The probability of a return falling within ± 2 standard deviations is 95.44%.

If you are promised a nominal return of 12% on a 1-year investment, and you expect the rate of inflation to be 3%, what real rate do you expect to earn?

Real rate = (1.12/1.03) - 1 = 8.74%

Which one of the following would be considered a risk-free asset in real terms as opposed to nominal?

U.S. T-bill whose return was indexed to inflation

The geometric average of -12%, 20%, and 25% is _________.

[(1 + −.12)(1 + .20)(1 + .25)]^(1/3) - 1 = 9.70%

The ______ measure of returns ignores compounding

arithmetic average

You have calculated the historical dollar-weighted return, annual geometric average return, and annual arithmetic average return. If you desire to forecast performance for next year, the best forecast will be given by the ________.

arithmetic average return

(NOT ON TEST) Two assets have the following expected returns and standard deviations when the risk-free rate is 5%: Asset A, E(ra)= 10%, σA = 20% Asset B, E(rb)= 15%, σB = 27% An investor with a risk aversion of A = 3 would find that _________________ on a risk-return basis.

neither asset A nor asset B is acceptable A= (E(r1)-Rf)/ σQ^2 Minimum Acceptable Return is given by E(rp)=(A * σQ^2)+rf For A: E(ra) =(3*.04)+.05=17% For B: E(rB)= (3*.729)+ .05=26.87%

You invest $1,000 in a complete portfolio. The complete portfolio is composed of a risky asset with an expected rate of return of 16% and a standard deviation of 20% and a Treasury bill with a rate of return of 6%. A portfolio that has an expected value in 1 year of $1,100 could be formed if you

$1,100 = y × (1,000)(1.16) + (1 - y)1,000(1.06), so y =.4 place 40% of your money in the risky portfolio and the rest in the risk-free asset

You are considering investing $1,000 in a complete portfolio. The complete portfolio is composed of Treasury bills that pay 5% and a risky portfolio, P, constructed with two risky securities, X and Y. The optimal weights of X and Y in P are 60% and 40%, respectively. X has an expected rate of return of 14%, and Y has an expected rate of return of 10%. To form a complete portfolio with an expected rate of return of 11%, you should invest __________ of your complete portfolio in Treasury bills

.11= Wf(.05)+(1-Wf)*{(.6)(.14)+(.4)(.10 Wf=.19

Your timing was good last year. You invested more in your portfolio right before prices went up, and you sold right before prices went down. In calculating historical performance measures, which one of the following will be the largest?

Dollar-weighted return

An investor invests 70% of her wealth in a risky asset with an expected rate of return of 15% and a variance of 5%, and she puts 30% in a Treasury bill that pays 5%. Her portfolio's expected rate of return and standard deviation are __________ and __________ respectively.

E(r) = .7(.15) + .3(.05) = .12 standard Dev rp=.70(.05)^.5= 15.7%

Your investment has a 40% chance of earning a 15% rate of return, a 50% chance of earning a 10% rate of return, and a 10% chance of losing 3%. What is the standard deviation of this investment?

E(rp)= (.4)(.15)+(.5)(.10)+(.10)(-.03)= 10.7% σP= .4(.15-.107)^2 + .5(10-.107)^ 2 +.10(-.03-.107)^2 σP= 5.14%

You have an APR of 7.5% with continuous compounding. The EAR is _____.

EAR = (e^(.075)) - 1 = 7.79%

In calculating the variance of a portfolio's returns, squaring the deviations from the mean results in: I. Preventing the sum of the deviations from always equaling zero II. Exaggerating the effects of large positive and negative deviations III. A number for which the unit is percentage of returns

I and II only

You invest $1,000 in a complete portfolio. The complete portfolio is composed of a risky asset with an expected rate of return of 16% and a standard deviation of 20% and a Treasury bill with a rate of return of 6%. The slope of the capital allocation line formed with the risky asset and the risk-free asset is approximately _________.

Slope = (16 - 6)/20 = .50

You invest $1,000 in a complete portfolio. The complete portfolio is composed of a risky asset with an expected rate of return of 16% and a standard deviation of 20% and a Treasury bill with a rate of return of 6%. __________ of your complete portfolio should be invested in the risky portfolio if you want your complete portfolio to have a standard deviation of 9%

σC = y × σp 9% = y × 20% y = 9/20 = 45%

The return on the risky portfolio is 15%. The risk-free rate, as well as the investor's borrowing rate, is 10%. The standard deviation of return on the risky portfolio is 20%. If the standard deviation on the complete portfolio is 25%, the expected return on the complete portfolio is _________.

σC = y × σp = .25 σC = y × .20 = .25 y = .25/.20 = 1.25 1 - y = -.25 E(rC) = 1.25 × 15% - .25 × 10% = 16.25%